When a user shares her data with online platforms, she reveals information about others in her social network. In such a setting, network externalities depress the price of data because once a user's information is leaked by others, she has less reason to protect her data and privacy. These depressed prices lead to excessive data sharing. We characterize conditions under which shutting down data markets improves welfare. Platform competition does not redress the problem of excessively low data prices and too much data sharing and may further reduce welfare. We propose a scheme based on mediated data sharing that improves efficiency.